How can I get people to like me?

I recall in Oblivion there was a speechcraft circley-type-thing that you could use to get people to like you more. Is that in Skyrim?

Or is there another way to get people to like me more?

The speechcraft circle isn't in Skyrim, sadly.

However, if the npc has quests, completing them increases their disposition towards you. I believe there is also a disposition increase if you are a member of their faction (such as the theives guild, etc).

Keep in mind not all npcs can be married. Some of them appear to have conditions for being marriageable, and you can see those at the UESP page for marriage.

And do not forget that you have to wear an amulet of mara if you want the option to marry someone to appear in the dialog.